And I tried to explain that the lumber analogy was flawed. I thought an integral/sum would work, being the simplest way to break down the problem, but apparently not. I tried providing an example of a torque with no secondary force (I provide another one below), since you only need to provide one example to disprove necessity, but that didn't seem to stick, either.

Try this: put your piece of lumber on a slick ice-rink (just after the Zamboni goes by) and kick it on the side at one end. It will slide away from you, spinning. *One* force (your foot hitting it), and there is torque.

What your door analogy misses is that the door would still spin "open", even if there were no force to hold it to the wall. You don't need two forces. The *net* force (vector sum of all forces acting on the object) just has to be not pointed at the center of mass. That's all you need.

True, in the Newtonian limit, but irrelevent. Silas covered this perfectly well already, so I won't repeat.

I agree with Gary. Arguments by authority are irrelevant. Let's stick to the math.

FWIW, I'm not angry, just baffled and frustrated.

And I would like to point out (again) that I have not quoted a single book.

And that's all I have to say about that.

Don